8-14.  A wide flange beam is used to support a vertical force  as shown in the figure. The beam is 20-ft long and pinned connected at both of its ends. The modulus of elasticity follows . Determine the distribution of the critical buckling load. Also, determine the probability of buckling. Assume that E and P are independent.

Solution:

Section roperties of the wide flange beam are

,    

Then, the critical axial buckling load is

;       .

Since , we have

Thus, the critical buckling load follows .                                       Ans.

Set , then , where

Thus, the probability of failure is

                     Ans.